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Results tagged with soft-question
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user 19276
Questions that are about research in mathematics, or about the job of a research mathematician, without being mathematical problems or statements in the strictest sense. Do not use this tag for easy or supposedly easy mathematical questions.
67
votes
Parodies of abstruse mathematical writing
Well there is C. E. Linderholm's Mathematics made difficult ("available on the internet")...
Also, if I remember well, D. Nordon's Les mathématiques pures n'existent pas! has a pretty biting parody o …
46
votes
What recent programmes to alter highly-entrenched mathematical terminology have succeeded, a...
Although just beyond your 50-year scope, this may be of interest. Among the series $\mathsf A_n, \mathsf B_n, \mathsf C_n, \mathsf D_n$ in the Cartan-Killing classification of simple Lie groups, every …
36
votes
Accepted
Etymology of "exterior" in "exterior calculus"
I think it's well known to have been introduced by Grassmann. He explains the word choice in Die lineale Ausdehnungslehre (1844, pp. x-xi):
I have shown how one can understand as product of two se …
- 31.5k
32
votes
Accepted
Famous cases of multiple papers by the same author published in same issue of same journal
Roger Howe famously filled an entire issue of Pacific Journal of Mathematics (volume 73, no.2, 1977) with 8 different papers. (Also, Euler...)
27
votes
Nontrivially fillable gaps in published proofs of major theorems
If a 25-year interlude will do, there is
R. F. Coleman has sent me his preprint ["Manin's proof of the Mordell conjecture'', Preprint, 1988; per bibl.] concerning my proof of Mordell's conjecture …
26
votes
What is the oldest open math problem outside of number theory?
Stability of the Solar System ?
(Question often attributed to Newton in Opticks, 1717 or 1730.)
To further specify as requested by Timothy Chow, make it a few ($3\leqslant N\leqslant 8$) planets under …
- 31.5k
24
votes
Mathematicians with both “very abstract” and “very applied” achievements
Several known for “pure” work have rather applied contributions to geometrical optics:
Carathéodory (1937) Geometrische Optik
Chaundy (1919) The aberrations of a symmetrical optical system
Whittaker …
20
votes
Accepted
Historically, which came first: the Lie algebras or their classification?
The classification came first. As Killing says in his introduction (translation by Coleman (1989)):
For each $l$ there are four structures supplemented for $l = 2, 4, 6, 7, 8$ by exceptional simpl …
- 31.5k
20
votes
Exceptional isomorphisms of Lie groups
Pencilled inside the back cover of my copy of Knapp's book is a picture that helps me keep a synoptic view of (all?) real form isomorphisms. It is the analog of summarizing the complex isogenies (alre …
- 31.5k
17
votes
Mathematicians with both “very abstract” and “very applied” achievements
I have a friend to whom De Rham was famous for completely different reasons — as author of a “corner-cutting algorithm” used in Computer Aided Geometric Design (of car bodies).
15
votes
Examples of research on how people perceive mathematical objects
Rudolf K. Luneburg, author of Mathematical Theory of Optics (1944), also published the book Mathematical analysis of binocular vision (Princeton UP, 1947) in which he argued that the "psychological sp …
- 31.5k
14
votes
What recent programmes to alter highly-entrenched mathematical terminology have succeeded, a...
From around 1900 to 1970, there was a highly-entrenched practice to write maps as $f:x\to y$ with an arrow between argument and value (e.g. Weyl 1913, p. 54).
Starting in the 1930s, a programme arose …
13
votes
Why doesn't mathematics collapse even though humans quite often make mistakes in their proofs?
Further to M. Shulman’s advice to “develop your intuition”, it’s probably worth adding that this is often done by understanding many examples, special cases whose moving parts are already transparent …
12
votes
Autobiographies of mathematicians
19th century as requested:
Charles Babbage, Passages from the life of a philosopher, 1864.
George Biddell Airy, Autobiography of Sir George Biddell Airy, 1896.
French scientists often wrote (and s …
12
votes
Have any long-suspected irrational numbers turned out to be rational?
Reviewer’s account of remarks of M. Duflo in On the Plancherel formula for almost algebraic real Lie groups (1984, p. 158), further confirmed in (1988, p. 328):
I find it amusing when the author p …